Phase-Transformation Fronts Evolution for Stress- and Strain-Controlled Tension Tests in TiNi Shape Memory Alloy

E.A. Pieczyska & S.P. Gadaj & W.K. Nowacki & H. Tobushi

Received: 13 October 2005 /Accepted: 17 March 2006 /Published online: 16 May 2006# Society for Experimental Mechanics 2006

Abstract Nucleation and development of phase trans-

formation fronts in TiNi shape memory alloy subjected

to the stress- and strain-controlled tension tests were

investigated. A thermovision camera was applied to

register the distribution of infrared radiation emitted

by the specimen and to find its temperature variations.

During the loading, narrow bands of considerably high-

er temperature corresponding to the martensitic phase,

starting from the central part of the specimen and

developing towards the specimen grips, under both

approaches, were registered. The inclined bands of

heterogeneous temperature distribution were observed

also during the unloading process of the SMA, while

the reverse transformation accompanied by tempera-

ture decrease took place. Thermomechanical aspects

of martensitic and reverse transformations for various

strain rates were analyzed under both stress- and

strain-controlled tests.

Keywords Shape memory alloy . Martensitic

transformation . Phase transformation front .

Temperature change . Stress-controlled test .

Strain-controlled test . Infrared thermography

Introduction

New functions and wide capabilities are expected by

multifunctional intelligent materials, possessing vari-

ous functions in differing environmental conditions [1,

2]. Among the various kinds of intelligent materials,

shape memory alloys (SMAs) characterized by a

complex combination of functions, like sensing, pro-

cessing and actuating functions, based on shape mem-

ory effect and superelasticity, are expected to be widely

applied in the near future [3]. Most widely used in

practical applications are TiNi SMAs which are

characterized by their excellent shape memory prop-

erties, sufficient strengths and ductility, high corrosion

resistance and good biocompatibility. These character-

istics enable SMAs to find applications in car, aircraft

and fine machine industries, daily equipment and

medicine [3–12].Under uniaxial loading of the TiNi SMA, the phase

transitions are often accompanied by unstable mechan-

ical behavior and localized transformation, resulting in

propagating transformation fronts. They are character-

ized by significant non-uniform deformation and tem-

perature fields. These phenomena have been studied

experimentally in detail in [13, 14] and the effects were

confirmed in [15–17]. The interesting results of the

localized phase transformation obtained for micro-

tubes were presented in [18, 19] and completed with a

proposed model in [20]. Two almost perpendicular

directions of the transformation bands, developing to-

wards the specimen grips, were observed using an in-

frared camera in [21–24]. The transformation-induced

stress relaxation effects were discussed in [23, 24].

Recoverable energy and dissipated strain energy were

evaluated under both temperature-controlled and

-uncontrolled conditions for various strain rates in [25].

An interesting model on the localized nucleation and

Experimental Mechanics (2006) 46: 531–542

DOI 10.1007/s11340-006-8351-y

E. A. Pieczyska ()) : S. P. Gadaj :W. K. NowackiInstitute of Fundamental Technological Research,Polish Academy of Sciences, Swietokrzyska 21,00-049 Warsaw, Polande-mail: epiecz@ippt.gov.pl

H. TobushiDepartment of Mechanical Engineering,AICHI Inst. of Technology, 1247, Yachigusa, Yakusa-cho,Toyota, Aichi 470-0392, Japane-mail: tobushi@aitech.ac.jp

E.A. Pieczyska (*) & S.P. Gadaj & W.K Nowacki

(SEM member)

SEM

propagation phenomena for the wide range of load-

ing rates and ambient thermal conditions was pre-

sented in [26]. Measurement of inhomogeneous

deformation behavior arising in SMA was described

in [27]. The thermal and calorimetric effects induced

by Luders bands propagation in steel, related also to

SMA, were analyzed in [28]. The conditions under

which the Luders-like deformation in SMA can be

observed, as well as can be eliminated, are specified in

details in [29]. However, based on the results pre-

sented in this paper, it is difficult to agree with all of

the above [29].

The objective of the work is the thermomechanical

aspect of the stress-induced phase transformations in

TiNi SMA, namely an investigation into the onset and

growth of the martensitic and the reverse transformation

fronts on the basis of contact-less specimen temperature

variations. Depending on the applications, the SMA

elements may be controlled by force or by displacement

and so the study comprises both the stress- and strain-

controlled conditions. The subloop deformation behav-

ior with cyclic loading, transformation-induced creep

and stress relaxation depend on strain rate and stress rate

[30]. Since the applied behaviors of SMAs are strongly

temperature dependent, a study of their thermomechan-

ical properties is of key value.

The investigations into measurements of the tem-

perature accompanying the deformation process of

SMAs have been launched quite recently [6–17]. At

first the temperature was estimated using a thermo-

couple, which, however, limited the measurement to

only a single chosen point [6]. Application of an

infrared technique allows monitoring of the tempera-

ture distribution on the examined specimen surface,

measurement of a mean temperature over a chosen

area, an arbitrarily chosen segment or chosen points

[13–17, 21–26, 28].

In the present paper, nucleation and development of

the martensite and reverse transformations fronts in

TiNi SMA subjected to various stress- and strain-

controlled tension tests using a smart thermovision

camera were investigated.

Experimental Procedure

The tension tests were carried out on a belt type spec-

imen of 160 � 10 � 0.4 mm, cut off from a strip of

TiNi SMA of the constitution Ti-55.3wt.% Ni and

characterized by the austenite finish temperature Af

equal to 283 K. Since the Af temperature is so low, the

TiNi SMA demonstrates a complete loop of pseudo-

elasticity during the tests carried out at room temper-

ature. Before the testing, the specimen surface was

covered with a very thin layer of carbon black powder

in order to make its emissivity higher and more

homogeneous. All investigations were performed at

room temperature of about 296 K. The specimens were

subjected to a strain-controlled tension test with

various strain rate and stress-controlled tension tests

with various stress rate in the quasi-static range of

deformation. In the course of investigations both the

mechanical characteristics and the distribution of the

infrared radiation emitted by the specimen surface were

continuously registered. The stress and the strain

quantities were related to the current (instantaneous)

value of the specimen cross-section and thickness

values. The temperature distribution was registered

by using infrared equipment allowing for infrared

photographs, i.e., thermograms, to be stored in digital

form with a maximal frequency of 50 Hz. That allows

reproduction of the images at any moment and makes

the calculation of temperature as well as its presenta-

tion straightforward. This can be presented as a func-

tion of time or other parameters of the deformation

process.

The infrared camera used is long wave type, work-

ing in the wave range of 7.5–13 2m. The matrices size

is 320 � 240 pixels. The spatial and the temper-

ature resolutions depend on the camera-specimen

distance. In the case of the measurement presented in

the paper, the distance was 10 cm and the spatial

resolution was 0.3 mm. The measurement temper-

ature sensitivity, in the range up to 30 K, is below

0.08 K.

For these investigations three kinds of temperature

registration were applied:

– temperature distribution on the specimen surface,

– mean temperature taken from the chosen speci-

men area,

– change in temperature of a chosen point on the

specimen surface.

The temperature distribution on the specimen sur-

face immediately reflects the origin and development

of the new phases, both martensite and reverse, due to

the significant temperature variations between the

parent and the new phase.

The average temperature was calculated over an area

of 8 � 60 mm, located in the central part of the spec-

imen. It was used in the thermomechanical coupling

analysis.

The point temperature was taken from the part of the

specimen surface where the first band of the higher

temperature related to the new, martensite phase was

noticed.

532 Exp Mech (2006) 46: 531–542

SEM

The temperature and mechanical data enable the

analysis of the nucleation process and further de-

velopment of both the martensitic and the reverse

transformations.

Superelastic Behavior of TiNi SMA DuringStress- and Strain-Controlled Tension Tests

with Various Strain Rates

The stress–strain curves for the strain rates of 5 � 10j4

sj1; 5 � 10j3 sj1, 5 � 10j2 sj1 and 10j1 sj1 under

strain-controlled conditions are shown in Fig. 1(a), and

the curves obtained under stress-controlled conditions

with the stress rates of 12.5, 25, 50 and 75 MPa sj1 are

shown in Fig. 1(b).

For all stress and strain rates, the pseudoelasticity

effects were registered for both approaches. After an

elastic deformation the martensitic transformation

starts. Its initial homogeneous stage, accompanied by

uniform, small temperature increase, is followed by the

waving part of the stress–strain curves, manifested by

shear-like bands with significant temperature rise,

similar to that observed in Luders inhomogeneous

deformation [13–29]. Next, the upswing region is

observed, manifested by a more advanced and more

homogeneous stage of the phase transformation,

accompanied by the more uniform temperature distri-

bution, (see next chapters).

During the process of unloading, after passing its

elastic stage, the reverse transition initiates. After it is

completed, the material almost returns to the parent

austenite phase. However, the residual strains, related

to a small amount of the residual martensite and ir-

reversible macro-structural changes appear, depending

on the specimen history.

Influence of Strain Rate on Mechanicaland Temperature Characteristics

The investigations conducted have proved that the run

of the stress–strain curves depends on the strain rate

applied under both approaches. However, the influence

of the strain rate is stronger for the strain-controlled

tests. During phase transformation, stress magnitudes

increase as the strain rate grows, since the temperature

increases while the deformation process develops [8, 9,

11–17]. The stress–strain curve developing at a very

low strain rate of 10j4 sj1 is almost flat, like the typical

curve illustrating the phenomenon of pseudo-elasticity

in SMAs, found for low strain rates [6, 11]. For higher

strain rates, the slope of inclination of the segments of

stress–strain curves, corresponding to the martensitic

and the reverse transformations is steeper. The higher

the strain rate, the steeper the slope of the curve.

Temperature changes vs. stress for TiNi SMA ob-

tained by the tension tests with various stress and strain

rates under the stress- and strain-controlled conditions

are presented in Fig. 2(a) and (b), respectively.

One can observe that the higher the strain rate the

higher the temperature change for both the stress- and

strain-controlled tests. After the initial homogeneous

range of deformation, a significant temperature in-

a) b)

0.00 0.02 0.04 0.06 0.08True strain

0

200

400

600

800

Tru

e st

ress

(M

Pa)

TiNi SMA

16

1718

19

16 - 12.5 MPa/s17 - 25.0 MPa/s18 - 50.0 Mpa/s19 - 75.0 MPa/s

>

<

< <

0.00 0.02 0.04 0.06 0.08True strain

0

200

400

600

800

Tru

e st

ress

(M

Pa)

TiNi SMA

ε = 10-1 s

-1

.

ε = 5*10-3 s

-1

.

ε = 5*10-4s-1.

.

ε = 5*10-2 s

-1

>

>>>

>

<

<<

<

Fig. 1. Stress-strain curves of TiNi SMA subjected to (a) strain-controlled tension tests with strain rates: 5�10j4 sj1; 5�10j3 sj1,5�10j2 sj1, 10j1 sj1, and (b) stress-controlled tension tests with stress rates: 12.5, 25, 50, 75 MPa sj1. (E. A. Pieczyska, S. P. Gadaj,W. K. Nowacki and H. Tobushi)

Exp Mech (2006) 46: 531–542 533

SEM

crease, related to the exothermic martensitic transfor-

mation, is observed. The highest temperature increase

is observed at the end of the martensitic transformation

and it changes from 26 to 40 K, depending on the strain

rate applied (Fig. 2). When unloading, the temperature

drops as the stress decreases. First, at the elastic un-

loading, a slow temperature decrease can be observed,

caused by heat exchange with the surroundings. Then,

the temperature drops rapidly due to the endothermic

reverse transformation. One can notice that the seg-

ments of the curves related to the martensite and the

reverse phase transformations are almost parallel to

each other, irrespective of the strain rate or stress rate

applied. After the reverse transformation is completed,

the temperature drops below the room temperature.

The lowest temperature drop of 9 K was found for the

stress-controlled test with the lowest stress rate of 12.5

MPa/s, caused by heat transfer and stronger grip in-

fluence under these conditions.

Theoretical Background and Conditions for Progress

of Martensitic and Reverse Phase Transformations

According to the constitutive relationships proposed

by Tanaka [4] and Tanaka et al. [5, 6], and applied by

Tobushi et al. [10] and Lin et al. [11], the deformation

behavior of SMA due to martensitic transformation

can be described as follows Fig. 3(a):

�� ¼ D"

� þ �T þW��; ð1Þ

where s, e and T represent the stress, strain and tem-

perature, respectively. The coefficients D and q repre-

sent the modulus of elasticity and the thermoelastic

constant, respectively. The quantity (4/D) represents

the strain range of the martensitic transformation. The

internal state variable x represents the volume fraction

of the martensite phase. In this way, the volume

fraction of the parent phase is 1jx. The dot over the

symbols denotes the time derivative. The transforma-

tion kinetics for the martensitic transformation can be

described by the formula:

��

1� � ¼ bMCMT�� bM�

� � 0 ð2Þ

and for the reverse transformation:

� ��

�¼ bACAT

�� bA�

� � 0 ð3Þ

The material parameters: bM, CM, bA and CA are

determined from the experiment, carried out at various

temperatures. Assuming the parameters constant:

��¼ 1� exp bMCM Ms � Tð Þ þ bM�f g ð4Þ

��¼ exp bACA As � Tð Þ þ bA�f g; ð5Þ

where Ms and As stand for the temperatures at which

the martensite transformation and the reverse transfor-

mation start under the stress-free conditions, respectively.

Fig. 2. Temperature changes vs. stress in TiNi SMA subjected to (a) strain-controlled tension test with strain rates 5�10j3 sj1, 10j2

sj1, 10j1 sj1, and (b) stress-controlled tension test with stress rates 12.5, 25, 50, 75 MPa sj1. (E. A. Pieczyska, S. P. Gadaj, W. K.Nowacki and H. Tobushi)

534 Exp Mech (2006) 46: 531–542

SEM

The starting and completing lines for the martensite

transformation can be expressed by the straight lines

with a slope of CM:

� ¼ CM T �Msð Þ ð6Þ

� ¼ CM T �Msð Þ � 2 ln 10=bM ð7Þ

The starting and completing lines for the austenite

transformation can be expressed by the straight lines

with a slope of CA:

� ¼ CA T �ASð Þ ð8Þ

� ¼ CA T �ASð Þ � 2 ln 10=bA ð9Þ

The transformation regions prescribed by the trans-

formation lines, according to the equations (6), (7), (8),

(9) are shown in Fig. 3(a).

The conditions for the progress of the martensitic

transformation, [equation (2)] become:

bMCMT�� bM�

�bM < 0; therefore : ð10Þ

d�

dTQCM for dT > 0; and

d�

dT� CM for dT < 0

ð11Þ

The conditions for the progress of the reverse

transformation, (equation 3) become:

bACAT�� bA�

�bA > 0; therefore : ð12Þ

d�

dT� CA for dT > 0 and

d�

dTCA for dT<0 ð13Þ

Based on the tests carried out with various strain rates

and, related to this, various temperature increments

shown in Fig. 2, the stress-temperature graphs in Fig. 3(b)

are proposed to estimate the general conditions for the

progress of the martensitic and reverse transformations

during the stress-induced phase transformation at room

temperature. The conditions for the start and finish of

the martensitic transformation are expressed by the

transformation lines Ms (Martensite start) and Mf

(Martensite finish), while the conditions for the start

and finish of the reverse transition are expressed by the

lines As (Austenite start) and Af (Austenite finish),

respectively. The transformation progresses in the strip

areas between the start and finish lines, respectively.

The Ms, Mf, As and Af lines are necessary to be

determined based on the data under low strain rate, i.e.,

under the quasi-static isothermal conditions. This con-

dition can be obtained under the strain rate below

1.7 � 10j4 sj1. In the case of a higher strain rate, not

only stress but also temperature increases due to the

martensitic phase transformation and decreases due to

the reverse transformation. If we take into account the

variation in temperature due to the martensitic transfor-

mation, these lines and the deformation behavior of the

material can be evaluated. That is, if the stress-temper-

ature data for different strain rates are plotted on the

same chart while considering the variation in tempera-

ture, these lines are located parallel to each other, that is,

the slopes of the lines take the same values [Fig. 2(a),

(b)]. The conditions for the start and finish of the

martensitic and reverse transitions presented in Fig.

3(b), expressed by the lines Ms and Mf and by the lines

As and Af, respectively, are only an estimation. Howev-

er, their run is in agreement to the obtained data for the

tests performed at various stress and strain rates,

according to the Clausius–Clapeyron formula.

Fig. 3. (a) Conditions for progress of martensitic and reversetransformations. (b) Estimated paths for progress of martensiticand reverse transformation in TiNi SMA under stress- andstrain-controlled tension tests with various stress and strainrates; Ms Martensite start, Mf martensite finish, As austenitestart, Af austenite finish. (E. A. Pieczyska, S. P. Gadaj, W. K.Nowacki and H. Tobushi)

Exp Mech (2006) 46: 531–542 535

SEM

Onset and Development of PhaseTransformation Fronts

Two tests were chosen, with the strain rate of 10j2 sj1

[Fig. 4(a)], and the stress rate of 25 MPa sj1 [Fig. 4(b)],

in order to analyze the onset and growth of the stress-

induced phase transformation fronts and to discuss the

similarities and the discrepancies between the stress- and

strain-controlled approaches. The temperature distribu-

tions for the tests are shown in thermograms in Fig. 6: the

left side for the strain-controlled test and the right side,

for the stress-controlled test, respectively. One can see

that the points corresponding to the thermograms

shown in Fig. 6 are marked on the stress–strain curves

(Fig. 4) and the numbers over thermograms correspond

to the points marked on Fig. 4(a), (b). The chosen ther-

mograms are very characteristic of the phenomena

occurring during the martensitic and the reverse trans-

formations. The graphs, shown in Fig. 5(a) prove why

such stress- and strain-controlled tests were taken into

consideration. Namely, the rate of deformation, which

seems to be mainly responsible for the transformation

conditions, is similar for just these two chosen tests

[Fig. 5(a)]. The segment of curve for the stress-controlled

test, related to the martensitic transformation, is parallel

to the segment of the strain-controlled curve. However,

Fig. 4. Stress-strain curves under strain and stress controlled conditions of TiNi SMA, with the strain rate (a) 10j2 sj1 and stressrate (b) 25 MPa sj1. (E. A. Pieczyska, S. P. Gadaj, W. K. Nowacki and H. Tobushi)

Fig. 5. Comparison of (a) strain vs. time and (b) strain rate vs. strain for progress of martensite and reverse transformations understrain and stress controlled tests. (E. A. Pieczyska, S. P. Gadaj, W. K. Nowacki and H. Tobushi)

536 Exp Mech (2006) 46: 531–542

SEM

Fig. 6. Temperature distribution of TiNi SMA subjected to tension test at room temperature with constant strain rate 10j2 sj1 (leftside) and constant stress rate 25 MPa/s (right side); numbers of thermograms correspond to points at the curves in Fig. 4: 1,2,3,4,5loading; 6,7,8 unloading. (E. A. Pieczyska, S. P. Gadaj, W. K. Nowacki and H. Tobushi)

Exp Mech (2006) 46: 531–542 537

SEM

Fig. 6. continued

538 Exp Mech (2006) 46: 531–542

SEM

during the reverse transformation the conformity is not

so good. The calculated discrepancies in the strain rates

are shown in Fig. 5(b). The strain range chosen for two

tests is also not equal. Nevertheless, just these tests

were taken into account due to the mechanical data

being similar and the thermograms of the phase-tran-

sitions phenomena turning out to be of best quality.

The uniform temperature distribution on the spec-

imen surface indicates the homogeneity of the stress

and the strain state along the specimen. Before tension

started, the temperature of the specimen was uniform

and equal to the ambient temperature of 296 K. At the

initial tension stage, i.e., as the stress increases to its

local maximum [see Fig. 4(a) and (b)], the tempera-

ture of the specimens surface grows. The thermal

image, however, remains almost uniform indicating the

homogeneous nature of the phase transformation

process at this initial stage under both approaches

[see Figs. 4, 6(1)]. During loading, the temperature

distribution became non-homogeneous; the increase of

temperature in some areas of the specimen was higher

than in others (Fig. 6).

When the true strain value reached 0.013, a line of

higher temperature evolving into a narrow band ap-

peared on the specimen surface proving the initiation of

the localized martensite transformation [Fig. 6(2)]. The

band made an angle of 48- with the direction of

tension. The temperature difference in the area where

the band appears is about 8 K, proving the rapid

nature of the process. As the tension proceeds the

band significantly widens and other bands appear at

first parallel and then inclined at the same angle but in

the opposite direction [Fig. 6(3)]. The highest temper-

ature was registered at the intersection of the bands.

However, the mean temperature of the specimen

surface also increased during the process.

At higher strain level, more and more lines evolving

into bands appear finally reaching the specimen grip

[Figs. 4, 6(4)]. Due to heat flow and the more advanced

process, the thermal image becomes more ambiguous.

At this stage of deformation, the wavy part of the

stress–strain curves, related to the onset and movement

of the bands, ends and is followed by the upswing region

of the curve. At the final phase of tension, the increase

in temperature exceeds 27 K for this strain rate (Fig. 2).

In the course of unloading, bands of significantly

lower temperature appear. They are, however, rather

uniformly distributed on the specimen surface, proving

that the reverse transformation also develops in an

inhomogeneous way [Fig. 6(6, 7, 8)]. The temperature

of the specimen at the end of unloading is lower than

Table 1

Martensitic

Transformation

Reverse

Transformation

$A $T $A $T

"� ¼ const +200 MPa +36 K j190 MPa j28 K�� ¼ const +270 MPa +26.5 K j240 MPa j21.5 K

Fig. 8. Localized phase transformation bands in TiNi SMAobserved in various techniques: (a) optical photograph of traceof the transformation bands on the specimen surface covered byspray with black lacquer, (b) optical photograph of relief of thetransformation bands on the specimen surface covered byblack marking ink, (c) infrared image of the transformation band.(E. A. Pieczyska, S. P. Gadaj, W. K. Nowacki and H. Tobushi)

Fig. 7. Temperature distribution of TiNi SMA after tension test with constant strain rate 10j2 sj1 (left side) and constant stress rate 25MPa/s (right side): A, ( = 0. (E. A. Pieczyska, S. P. Gadaj, W. K. Nowacki and H. Tobushi)

Exp Mech (2006) 46: 531–542 539

SEM

the initial temperature of the specimen, before testing

[Figs. 2, 6(8)].

After the unloading is completed, the temperature

distribution still remained heterogeneous (Fig. 7)

which could be explained in the following way. After

unloading, some residual martensite remained. That is,

though the reverse transformation was completed

macroscopically, it was not completed microscopically.

Based on this residual martensite, residual or internal

stress after unloading might appear. Therefore, some

local microscopic reverse transformation still occurs

after the macroscopic completion of the reverse transi-

tion. Due to this effect, heterogeneous temperature

distribution may appear after unloading. This point will

be studied in more details during future research on the

cyclic tests performed on the same TiNi SMA.

Discussion

The phase transformation processes are strongly

temperature dependent. In the deformations occurring

within the range of quasi-static strain rates, some heat

is released during the martensitic transformation that

involves an increase in the specimen temperature. The

changes in the material temperature, in turn, affect a

stress increase in the specimen during the martensitic

transformation. The influence also appears on the

behavior of the s(e) curves (Fig. 1). Similar phenom-

ena, however in the opposite direction, can be ob-

served during the unloading process, when the reverse

transformation takes place. As a result both the stress

level and the shape of stress–strain curves depend

crucially on the strain rate applied and, related to this,

the specimen temperature. The run of the curves

depends on the temperature conditions, according to

the SMA Af temperature, as well as on the current

temperature of the specimen, caused both by heat

production and heat transfer. In this way, the pre-

sented curves differ from those obtained under the

temperature-controlled conditions [10], i.e., the stress

Fig. 9. True strain and temperature changes vs. time of TiNi SMA subjected to (a) strain controlled test—10j2 sj1; (b) stresscontrolled test—25 MPa/s ; $T Average temperature change from the specimen surface, $TP temperature change in the point wherethe martensite transformation start was noticed. (E. A. Pieczyska, S. P. Gadaj, W. K. Nowacki and H. Tobushi)

Fig. 10. Three stages of phase transformations: M1, M2 and M3distinguished on the stress and temperature vs. strain curves forTiNi SMA subjected to tension test with the strain rate of 10j2 sj1:$T Average temperature change in the testing area, $TP

temperature change at the point where the phase transition startwas noticed. (E. A. Pieczyska, S. P. Gadaj, W. K. Nowacki and H.Tobushi)

540 Exp Mech (2006) 46: 531–542

SEM

level is higher for the higher strain rates and signif-

icantly steeper [21, 22]. Therefore, energy dissipation

related to the phase transformations also changes

depending on the strain rate and the test conditions.

This was discussed in [25]. The estimated values in the

stress $A and the temperature $T variations due to the

inhomogeneous martensitic and the reverse transforma-

tions taken for the maximal stress rate and the strain

rate applied for the strain- and stress-controlled tests

are shown in Table 1. The data were taken from the

temperature vs. stress curves presented in Fig. 2(a) and

(b), respectively.

It can be concluded on the grounds of the obtained

results that no significant difference was observed

between stress- and the strain-controlled conditions,

according to the transformation bands onset and

development. For all the strain rates applied in both

approaches the martensitic and the reverse trans-

formations in TiNi SMA are inhomogeneous process-

es. The narrow inclined Luders-like bands of the

martensitic phase are observed starting from the cen-

tral part of the specimen and developing towards the

specimen grips. They are characterized by a tempera-

ture increase of 8 K and inclination towards the

tension direction of 48-. The phenomenon is so strong

that the bands can also be observed directly by the

naked eye on the specimen surface covered by lacquer

or marking ink (Fig. 8).

During the stress-controlled tests, almost immediate-

ly and at several points on the specimen surface, the

bands related to the new phase appear and they are

wider. Temperature distributions are more uniform and

the changes are smoother [Fig. 2(b), Fig. 6 right side].

This is also confirmed by the average and the point

temperature changes [Fig. 9(a) and (b)] when the

discrepancies between the temperature variations at

the point and the average temperature are smaller in

the stress-controlled conditions. So the whole process

of the martensitic and the reverse transformation

seems to be more homogeneous.

Based on mechanical and temperature character-

istics, the three stages of the phase transformation can

be distinguished during the TiNi SMA loading (Fig. 10):

M1 homogeneous, characterized by uniform small

temperature increase, M2 heterogeneous, manifested

by Luders-like bands of higher temperature, and

finally M3 almost homogeneous again, related to the

significant but more uniform temperature increase. The

reverse transition occurs also in an inhomogeneous way,

which was confirmed by the non-uniform temperature

distributions registered during unloading of the TiNi

SMA under both the stress- and strain-controlled

conditions.

Conclusions

During the stress-induced phase transformations in

TiNi SMA subjected to the temperature-uncontrolled

tests, stress increases as the strain rate grows under

both the stress- and strain-controlled conditions.

For both the approaches, the thermomechanical

behavior of the SMA confirms the exothermic charac-

ter of the austenite into martensite transformation and

the endothermic character of the reverse transforma-

tion. The average temperature changes are up to 40 K

for the highest strain rate applied.

Based on mechanical and temperature character-

istics, the three stages of the phase transformation can

be distinguished during the TiNi SMA loading: the

homogeneous stage, characterized by a uniform, small

temperature increase, the second heterogeneous stage,

manifested by the Luders-like bands of higher tem-

perature, and the finally almost homogeneous stage,

related to significant but more uniform temperature

distribution. The reverse transitions also occurs in the

inhomogeneous way, which was confirmed by the non-

uniform temperature distributions registered during

unloading of the TiNi SMA under both the stress- and

strain-controlled conditions.

For both the approaches, the narrow bands of

significantly higher temperature, related to the nucle-

ation of the martensitic phase, or lower tempera-

ture, related to the reverse one, similar to the Luders

bands, were observed to start from the central part of

the specimen and to develop towards the specimen

grips.

The bands of the new phase, characterized by the

angle of inclination with the direction of tension 48-

and the variation in temperature of about 8 K, were

followed by the next generation of the bands inclined

at the same angle but in the opposite direction.

The more advanced phase transformation is related

to the upswing region of the stress vs. strain curve,

when the martensitic transformation was more homo-

geneous and both the mechanical as well the temper-

ature curves were almost smooth.

Some discrepancies observed between the stress- and

the strain-controlled tests were caused by the various

instantaneous strain rates and related to the different

heat transfer conditions and stronger grip influence.

Acknowledgments This research has been carried out with thesupport of Polish Grant No. 4T08A06024, the JSPS Grants:No.13650104(C), Post-doc PO4774, Joint Research supported byJSPS and PAS: No. 6612. The authors also would like to thankProf. B. Raniecki (IFTR) and Prof. S. Miyazaki (Tsukuba Univ.)for fruitful discussions, as well as to extend their gratitude to L.Urbanski (IFTR), K. Hoshio and other students of AIT Japan,for technical advice.

Exp Mech (2006) 46: 531–542 541

SEM

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